35.3 Content
35.3.1 Maxwell’s Electromagnetic Theory
James Clerk Maxwell unified electricity and magnetism into a single theory (1865):
- Changing electric fields create magnetic fields
- Changing magnetic fields create electric fields
- These oscillations can propagate through space as waves
Maxwell calculated the speed of these waves:
\[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3.00 \times 10^8\ \text{m/s}\]
This matched the measured speed of light—proving that light is an electromagnetic wave.
35.3.2 The Wave Equation
All electromagnetic waves obey:
\[c = f\lambda\]
where: - \(c = 3.00 \times 10^8\) m/s (in vacuum) - \(f\) = frequency (Hz) - \(\lambda\) = wavelength (m)
All EM waves travel at the same speed in vacuum. Higher frequency means shorter wavelength.
35.3.3 Interactive: Electromagnetic Spectrum
| Region | Wavelength Range | Frequency Range |
|---|---|---|
| Radio | > 1 m | < 300 MHz |
| Microwave | 1 mm – 1 m | 300 MHz – 300 GHz |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz |
| Visible | 400 – 700 nm | 430 – 750 THz |
| Ultraviolet | 10 – 400 nm | 750 THz – 30 PHz |
| X-ray | 0.01 – 10 nm | 30 PHz – 30 EHz |
| Gamma | < 0.01 nm | > 30 EHz |
35.3.4 Measuring the Speed of Light
Roemer (1676): Used timing variations of Jupiter’s moons to estimate c ≈ 2.2 × 10⁸ m/s
Fizeau (1849): Reflected light off a mirror 8.6 km away through a rotating toothed wheel. Got c ≈ 3.13 × 10⁸ m/s
Foucault (1862): Used rotating mirrors for more precision. Got c ≈ 2.98 × 10⁸ m/s
Modern value: \(c = 299,792,458\) m/s (exact, defines the metre)
35.3.5 Spectroscopy
Spectroscopy is the study of light spectra to identify materials and their properties.
Types of spectra: - Continuous spectrum: Hot dense object (black body) - Emission spectrum: Hot low-density gas (bright lines) - Absorption spectrum: Cool gas in front of hot source (dark lines)
Each element has a unique pattern of spectral lines—like a fingerprint. This allows identification of elements in distant stars.
35.3.6 Interactive: Spectral Lines
35.3.7 Wien’s Displacement Law
The peak wavelength of a black body spectrum depends on temperature:
\[\lambda_{max} = \frac{b}{T}\]
where: - \(\lambda_{max}\) = peak wavelength (m) - \(b = 2.90 \times 10^{-3}\) m·K (Wien’s constant) - \(T\) = absolute temperature (K)
- Hot stars (T > 10,000 K) → peak in UV/blue → appear blue-white
- Medium stars (T ≈ 6000 K) → peak in visible → appear yellow
- Cool stars (T < 4000 K) → peak in red/IR → appear red
35.3.8 Doppler Effect for Light
When a source moves relative to an observer, wavelengths shift:
\[\frac{\Delta\lambda}{\lambda} = \frac{v}{c}\]
- Redshift: Source moving away → wavelength increases
- Blueshift: Source approaching → wavelength decreases
This allows measurement of stellar velocities.